Localized synchronous patterns in weakly coupled bistable oscillators

Abstract

Motivated by numerical continuation studies of coupled mechanical oscillators, we investigate branches of localized time-periodic solutions of one-dimensional chains of coupled oscillators. We focus on Ginzburg--Landau equations with nonlinearities of Lambda-Omega type and establish the existence of localized synchrony patterns in the case of weak coupling and weak-amplitude dependence of the oscillator periods. Depending on the coupling, localized synchrony patterns lie on a discrete stack of isola branches or on a single connected snaking branch.

17 pages, 7 figures

References in corpus (7)

• Discrete Breathers
• Dark solitons, modulation instability and breathers in a chain of weakly non-linear oscillators with cyclic symmetry
• Existence and spectral stability of multi-pulses in discrete Hamiltonian lattice systems
• Nucleation and propagation of excitation fronts in self-excited systems
• Standing Wave Solutions in Twisted Multicore Fibers
• Rotating Wave Solutions to Lattice Dynamical Systems II: Persistence Results
• Stable Periodic Solutions to Lambda-Omega Lattice Dynamical Systems